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If for two vectors hat(A) and hat(B),sum...

If for two vectors `hat(A)` and `hat(B)`,sum `(vec(A)+vec(B))` is perpendicular to the diffrence `(vec(A)-vec(B))`. Find the ratio of their magnitude.

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To solve the problem where the sum of two vectors \( \vec{A} \) and \( \vec{B} \) is perpendicular to their difference, we can follow these steps: ### Step-by-Step Solution: 1. **Understanding the Condition**: We know that two vectors \( \vec{A} + \vec{B} \) and \( \vec{A} - \vec{B} \) are perpendicular. This means that their dot product is zero: \[ (\vec{A} + \vec{B}) \cdot (\vec{A} - \vec{B}) = 0 ...
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